Mistakes are valuable. So says a sign on the wall in Robert Sears’ mathematics classroom. It is one of a dozen or more signs around the room reminding students that mathematics is not a linear path to answers, but an interconnected web of questions. Sears says the most interesting conversations in his class often center on mistakes or failed approaches to a problem. Says Sears, “A mistake means there is an identifiable disconnect between our current understanding and what we are being asked to do, which is where we can make new connections and are primed to learn our best.” A big focus of Sears’ 7th and 8th grade math classes at Hillbrook is helping students embrace their mistakes and the mistakes of others, so that they can learn.
A typical day in his 8th grade Algebra class starts with students reviewing their homework by individually demonstrating how to solve a given problem on the whiteboards around the room. The atmosphere is relaxed and collaborative. There is no shame in getting stuck. Students chime in with ideas, or go up to the whiteboards to help one another. “How are we feeling about that shortcut?” he asks the room, “does that make it easier or more confusing?” Students chime in with opinions, most agreeing it is easier with the shortcut. The goal for students is not simply finding solutions to problems, but knowing how to get there. “Give me two reasons why you know the answer to this problem,” Sears asks his students. Often students work out problems out loud, or with one another. “If you expand the numbers it makes it easier to understand, but it takes a long time to write it out,” says one student to his tablemates. Upon discovering the patterns in three different equations on the board, another student is heard exclaiming, “Whoa, that is so cool!”
8th grader Freya Y. shares that this spirit of collaboration and problem solving in middle school math helps to foster not only academic grit but collegiality: “The rule for homework in my class is to try as hard as you can and if you get stumped, write down your questions. When we come into class, we take turns presenting the questions we had and then discuss strategies and solutions as a group. This way of learning helps me tremendously for a couple different reasons: One, I always know that as long as I try my best on homework, I always have something to contribute to the class whether it is a question or an answer. Two, if I ever feel stuck or frustrated, I have a group of fellow students and a teacher around me to help explain solutions; I never feel like I am working all alone. I never have to worry about being made fun of for a wrong answer. It really is a safe space and I know that everyone in the room with me is there to support me and I am there to do the same for everyone.”
Collaboration is one of the hallmarks of Hillbrook’s approach to mathematics, along with sense-making and problem-solving. Sears says students learn how to explain the processes they are using instead of simply memorizing steps. “We like to see math as a tool to solve problems rather than an end in itself. We want students to be able to solve a math problem using multiple approaches, and to approach unfamiliar problems with patience and creativity.”
Patience can be tough to muster in middle school, especially when faced with new challenges. “Students can forget that math is essentially common sense,” says Sears. “When things get a little too complicated, it can seem like just a series of mysterious, confusing steps. More often than not, clarifying terms and approaching a problem in a way that makes sense to the student, even if it’s a less efficient method, paves the way for a more clear understanding,” he explains. Helping students “remain calm and calculate on” is part of the process for Sears, and it probably helps that as a teacher, he is not easily rattled.
This soft-spoken father of three says he got into teaching after the September 11th terrorist attacks on the United States. “I was living in New York City and had recently finished my undergraduate degree and was planning on going to law school. During that time, I decided that I needed to do something I was really passionate about, and teaching is something that always interested me, but I hadn’t yet considered going in to it seriously.” Sears applied to the New York City Teaching Fellows, a two-year program similar to Teach for America. He had planned on teaching for only two years, but fell in love with the craft of teaching, “Teaching in New York also introduced me to people, both students and colleagues, as well as parts of the city that I would never have been exposed to otherwise. I got to know an enormously diverse group of people and a wide variety of schools,” he says. When the family decided to move back to California, Sears was excited to find Hillbrook, which he says combined some of the best elements of schools he had seen.
Over the years from New York to California, Sears has taught 6th through 12th grades, but finds a lot to love about middle school, “I’m drawn to middle school because of the energy of the students, and the palpable excitement when they make sense of a new concept or master a new skill. I also think it’s an important time in the students’ life, when they are forming their identities. It is so important for learning, especially in math, to be understood as something they can engage in, find success in, and take ownership of.”
Sears says he wants his students to feel empowered in and to know that they can approach any problem, even ones that seem daunting at first. Says Sears, “I like to think of math as an introduction to philosophy. Even in 8th grade algebra, we can use careful reasoning to understand ideas as abstract as the existence of irrational numbers or ideas of the infinite.”
This 2018-19 school year at Hillbrook has been especially impactful for Sears because of the changes to the schedule which allow for longer, integrated blocks. In middle school, these integrated classes weave together lessons from different disciplines such as mathematics and science, English, world language, or art. Sears and his colleagues work together to teach these large, extended classes. Sears says in this way, Hillbrook is helping students make connections with mathematics and other subjects. When students see that mathematical principles also apply to art, science, English, or any other curricula, Sears says it deepens understanding and engagement across the board.
The student experience in middle school math affirms that encouraging children to collaborate, and to think creativity (and with collegiality), gives them the tools to apply these principles to higher level math and to other areas of their academic and personal lives where problem solving skills are needed.
8th grader Ruby R. reflects, “My learning this year has exponentially helped me solve problems in and out of school. With Mr. Sears in particular, he encourages you to think outside of the box and look at each problem in a new light. With this style of learning, the thought of conquering more difficult struggles doesn’t seem as overwhelming. I hope to bring this learning with me to high school.”
Freya concludes, “This system for learning math helps me learn the basics of geometry and simultaneously prepares me for my future learning endeavors.” She continues, “As I go off to high school next year I am prepared for anything math classes can throw at me. I know how to find help when I’m stuck, problem solve by myself and contribute to the overall knowledge of the class.”
Jeffrey Edsall, who graduated from Hillbrook in 2015 and went on to study advanced math at Los Gatos High School, and was recently accepted to continue his studies at Stanford University this fall confirms that the experiences, practices, and culture solidified in middle school math helped carry him beyond his years at Hillbrook: “Mr. Sears’ engaging and fun teaching style helped me become confident when facing complex problems and has prepared me with a foundation that has allowed me to succeed in my high school classes.”
Sears and his wife, Kadria, have three Hillbrook students of their own, Ida and Hunter in first grade and Henry in fourth grade, so he understands how math can be challenging for students and at times, for parents, too. It can be difficult trying to help your child if they are struggling with homework, or being patient if their path to understanding mathematics gets bumpy. Sears’ advice to parents is to try to let go a bit, “Let students learn math in their own terms, and be as socratic as possible. For parents who are good at math, it can be very tempting to share algebraic shortcuts. We want to avoid the experience of math as simply applying rules without understanding why.” Sears says there are bigger lessons being learned as a student grapples with understanding new concepts, “If we are helping students to become lifelong learners, then confidence, resourcefulness, and grit in the face of new challenges are most important.” Which leads to Sears’ favorite quote on the wall. This one isn’t specific to mathematics, but comes from Frederick Douglass, “If there is no struggle, there is no progress.”